The United States has made a commitment to go back to the moon to stay in the early part of the next century. In order to achieve this objective it became evident to NASA that a Lunar Outpost will be needed to house scientists and astronauts who will be living on the moon for extended periods of time. A study has been undertaken by the authors and supported by NASA to study the feasibility of using lunar regolith with different binders such as molten sulfur, epoxy or hydraulic cement as a construction material for different lunar structures. The basic premise of this study is that it will be more logical and cost effective to manufacture lunar construction materials utilizing indigenous resources rather than transporting needed materials from earth. Lunar concrete (made from Hydraulic Cement and lunar soil) has been studied and suggested as the construction material of choice for some of the lunar projects. Unfortunately, its hydration requires water which is going to be a precious commodity on the moon. Therefore this study explores the feasibility of using binders other than hydraulic cement such as sulfur or epoxy with lunar regolith as a construction material. This report describes findings of this study which deals specifically with using molten sulfur as a binder for Lunar concrete. It describes laboratory experiments in which the sulfur to lunar soil simulant ratios by weight were varied to study the minimum amount of sulfur required to produce a particular strength. The compressive and tensile strengths of these mixes were evaluated. Metal and fiber glass fibers were added to some of the mixes to study their effects on the compressive and tensile strengths. This report also describes experiments where the sulfur is melted and mixed with the lunar regolith in a specially designed vacuum chamber. The properties of the produced concrete were compared to those of concrete produced under normal pressure.